On the other hand, in Ref.[1]}, we perform detailed investigations of the \(\bar{D}\Sigma _c\) , \(\bar{D}\Sigma _c^*\) , \(\bar{D}^{*}\Sigma _c\)  and \(\bar{D}^{*}\Sigma _c^*\)  pentaquark molecular states
with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 13 in a consistent way.
The theoretical predictions of the molecule masses favor assigning the \(P_c(4312)\)  to be the \(\bar{D}\Sigma _c\)  pentaquark molecular state with the spin-parity \(J^P={\frac{1}{2}}^-\) , assigning the \(P_c(4380)\)  to be the \(\bar{D}\Sigma _c^*\)  pentaquark molecular state with the spin-parity \(J^P={\frac{3}{2}}^-\) , and assigning the \(P_c(4440/4457)\)  to be the \(\bar{D}^{*}\Sigma _c\)  pentaquark molecular state with the spin-parity \(J^P={\frac{3}{2}}^-\)  or the \(\bar{D}^{*}\Sigma _c^*\)  pentaquark molecular state with the spin-parity \(J^P={\frac{5}{2}}^-\) , respectively. In the works of other theoretical groups, the \(P_c(4312)\) , \(P_c(4380)\) , \(P_c(4440)\)  and \(P_c(4457)\)  are taken as the pentaquark molecular states, and their masses are studied with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of the dimension 8 [2]}, [3]}, [4]} or 6 [5]}. The works on the decay widths of the \(P_c(4312)\) , \(P_c(4380)\) , \(P_c(4440)\)  and \(P_c(4457)\)  are few, in Ref.[6]} and Ref.[7]}, the \(P_c(4312)\)  is assigned to be the pentaquark molecular state, its two-body strong decays are studied with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 10 and 8, respectively; while in Ref.[8]}, the \(P_c(4380)\)  is assigned to be the pentaquark molecular state, its two-body strong decays are studied with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 6.
